Generalised Gibbs Ensemble for spherically constrained harmonic models

Generalised Gibbs Ensemble for spherically constrained harmonic models

Blog Article

We build and analytically calculate the Generalised Gibbs Ensemble partition function of the integrable Soft Neumann Model.This is the model of a classical particle which is constrained to move, on average over the initial conditions, on an $N$ dimensional sphere, and feels clairemax nude the effect of anisotropic harmonic potentials.We derive all relevant averaged static observables in the (thermodynamic) $N ightarrowinfty$ limit.We compare them to their long-term dynamic averages finding excellent agreement in all phases 14765-prb-a01 of a non-trivial phase diagram determined by the characteristics of the initial conditions and the amount of energy injected or extracted in an instantaneous quench.

We discuss the implications of our results for the proper Neumann model in which the spherical constraint is imposed strictly.